Download Factor Theorem and Remainder Theorem

Pure Core 1 Assessed Homework 5: Factor Theorem and
Remainder Theorem
1) Find the remainder when 2x³ - 9x² + 7x + 6 is divided by
(x – 4)
(3)
2) Use algebraic long division to find the remainder when
3x³ + 4x² - 6x + 3 is divided by (x -5)
(4)
3) a) Use the factor theorem to find one factor of
f(x) = x³ + 4x² +x – 6
(2)
b) Use algebraic long division to express f(x) in the form
(x + a) (bx² + cx +d)
(3)
c) Factorise f(x) completely
(3)
4) a) Given that x4 – 5x² + bx - 4 has a remainder of -4 when
divided by x + 2 find the value of b
(3)
b) Find the remainder when the expression is divided by
(x – 3)
(2)
5) a) Given that (x – 1) is a factor of f(x) where
f(x) = x³ - 4x² - kx +10 show that k = 7
(3)
b) Divide f(x) by (x – 1) to find a quadratic factor of f(x)
(3)
c) Write f(x) as a product of three linear factors
(2)
d) Calculate the remainder f(x) is divided by (x – 2)
(2)